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Boundedness criteria for a class of second order nonlinear differential equations with delay

Daniel O. AdamsMathew O. OmeikeIdowu A. OsinugaBiodun S. Badmus — 2023

Mathematica Bohemica

We consider certain class of second order nonlinear nonautonomous delay differential equations of the form a ( t ) x ' ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) and ( a ( t ) x ' ) ' + b ( t ) g ( x , x ' ) + c ( t ) h ( x ( t - r ) ) m ( x ' ) = p ( t , x , x ' ) , where a , b , c , g , h , m and p are real valued functions which depend at most on the arguments displayed explicitly and r is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski functional to establish our results. This work...

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